Answer:
B. 33
Explanation:
Step 1: Find total measure of ∠R:
- Since we're told that ∠R and ∠Q are bisected by RB and QA, the two angles are divided into two congruent angles.
- Therefore, the 38° is 1/2 the total measure of ∠R
- Thus, entire measure of R is 76 as 38 + 38 = 76.
Step 2: Find total measure, m, of ∠Q:
- The sum of the measures of the interior angles of a triangle always equals 180.
- Thus, we can find the measure of ∠Q by subtracting the sum of the measures of ∠R and ∠P from 180:
m∠P + m∠Q + m∠R = 180
m∠Q = 180 - (m∠P + m∠R)
m∠Q = 180 - (60 + 76)
m∠Q = 180 - 136
m∠Q = 44°
Since QA bisects ∠Q into two congruent angles, we divide 44 by 2 to find the measures of each angle made by the bisector: 44/2 = 22.
Step 3: Find x by setting the sum of the 38° angle, the 22° angle, and angle C equal to 180:
38 + (3x + 21) + 22 = 180
60 + 3x + 21 = 180
81 + 3x = 180
3x = 99
x = 33
Thus, x equals 33.